#WinBUGS codes generated by BAUW: http://bauw.psychstat.org
#USE WITH CAUTION!

Model{
  # Model specification for 1PL item response model
  for (i in 1:N){
    for (j in 1:20){
      y[i, j] ~ dcat(p[i,j,1:4])
     p[i,j, 1] <-q[i,j,1]
     q[i,j, 1] <-phi(tau[j,1]- (theta[i] - beta[j])*alpha[j])
     q[i,j, 2] <-phi(tau[j,2]- (theta[i] - beta[j])*alpha[j])
     q[i,j, 3] <-phi(tau[j,3]- (theta[i] - beta[j])*alpha[j])
     p[i,j,2]<-q[i,j,2]-q[i,j,1]
     p[i,j,3]<-q[i,j,3]-q[i,j,2]
     p[i,j,4]<-1- q[i,j,3]
    }
    theta[i] ~ dnorm(0, 1)
  }

  #Priors for model parameter
  b[1:80]~dmnorm(b0[],Pre_cov[])
}

# The (naive) starting values for model parameters.
list(beta=c(0))